## Example

The market for cookies is huge, with many consumers and many sellers.

The supply follows the equation `Q_S = 3 P`.

The demand follows the equation `Q_D = 10 - 2 P`.

In equilibrium, supply equals demand

$$ \begin{align*} Q_S &= Q_D \\ 3 P &= 10 - 2 P \\ 5 P &= 10 \\ P &= 2 \end{align*} $$In equilibrium, a banana is sold $2 and there are 6 bananas on the market.

### Question

The supply equation for bananas is `Q_S = -15 + 30 P`.

The demand is `Q_D = 80 - 65 P`.

What is the equilibrium price? What is the equilibrium quantity?

### Step 1: Equate supply and demand

###
##

$$
\begin{align*}
Q_S &= Q_D \\
-15 + 30 P &= 80 - 65 P \\
65 P + 30 P &= 80 + 15 \\
(65 + 30) P &= 80 + 15 \\
P &= \frac{80 + 15}{65 + 30} \\
P &= 1.0
\end{align*}
$$

$$
\begin{align*}
Q_S &= Q_D \\
-15 + 30 P &= 80 - 65 P \\
65 P + 30 P &= 80 + 15 \\
(65 + 30) P &= 80 + 15 \\
P &= \frac{80 + 15}{65 + 30} \\
P &= 1.0
\end{align*}
$$

### Step 2: Plug into the supply curve (or the demand curve)

###
##

$$
\begin{align*}
Q_S &= -15 + 30 \times 1.0 \\
Q_S &= 15.0
\end{align*}
$$

$$
\begin{align*}
Q_S &= -15 + 30 \times 1.0 \\
Q_S &= 15.0
\end{align*}
$$